Three concentric charged metallic spherical shells $A$,$B$,and $C$ have radii $a$,$b$,and $c$ (where $a < b < c$) and surface charge densities $+\sigma$,$-\sigma$,and $+\sigma$ respectively. The potential $V_A$ at the surface of shell $A$ is ($\epsilon_0$ = permittivity of free space).

A charge $+q$ is fixed at each of the points $x = x_0, x = 3x_0, x = 5x_0, \dots, \infty$ on the $x$-axis, and a charge $-q$ is fixed at each of the points $x = 2x_0, x = 4x_0, x = 6x_0, \dots, \infty$. Here $x_0$ is a positive constant. Take the electric potential at a point due to a charge $Q$ at a distance $r$ from it to be $Q/(4\pi\varepsilon_0 r)$. Then, the potential at the origin due to the above system of charges is:

Write an equation for the electric potential due to a volume charge distribution.

Two point charges $q_1 = 4 \times 10^{-8} \ C$ and $q_2 = -6 \times 10^{-8} \ C$ are placed at points $A$ and $B$ respectively,which are $50 \ cm$ apart. At what distance from point $A$ on the line $AB$ is the electric potential zero (in $cm$)?

Two thin concentric hollow conducting spheres of radii $R_1$ and $R_2$ bear charges $Q_1$ and $Q_2$ respectively. If $R_1 < R_2$,then the potential of a point at a distance $r$ from the centre $(R_1 < r < R_2)$ is

$A, B$ and $C$ are three points in a uniform electric field as shown in the figure. The electric potential is